where \(B\)  is the Bures metric [1]} between positive definite matrices and can be calculated as follows,
\(B(\sigma _{s,i}, \sigma _{t,j})^2 = tr(\sigma _{s,i} + \sigma _{t,j} - 2(\sigma _{s,i}^{1/2}\sigma _{t,j}\sigma _{s,i}^{1/2} )^{1/2}),\) 
